The Hawk latched onto the former Russian cruise ship Wednesday around 6:15 p.m.
It was successful in pulling the vessel away from offshore oil installations.
The Hawk and the Orlova are heading north, and are approximately 90 kilometres north of the Sea Rose platform.
Husky Energy operates the Atlantic Hawk. A spokeperson from the company said they will continue towing the Orlova until Transport Canada makes a decision about the vessel's final destination.
Husky said it isn't clear at this point, who will be footing the bill for the operation.